सोडोवचें sqrt{0.1(-14.5%)^2+0.3(-2.5%)^2+0.4(2.5%)^2+0.2(5.5%)^2}

$$\sqrt { 0.1 ( - 14.5 \% ) ^ { 2 } + 0.3 ( - 2.5 \% ) ^ { 2 } + 0.4 ( 2.5 \% ) ^ { 2 } + 0.2 ( 5.5 \% ) ^ { 2 } }$$

मूल्यांकन करचें

$$\frac{\sqrt{3145}}{1000}\approx 0.0560803$$

सोडोवणी पांवडे

10 न्युमरेटर आनी डिनोमिनेटर दोनूय गुणून \frac{14.5}{100} विस्तारीत करचो.

$$\sqrt{0.1\left(-\frac{145}{1000}\right)^{2}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

5 भायर काडून आनी रद्द करून एकदम उण्या संज्ञेत अपुर्णांक \frac{145}{1000} उणो करचो.

$$\sqrt{0.1\left(-\frac{29}{200}\right)^{2}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

\frac{841}{40000} मेळोवंक 2 चो -\frac{29}{200} पॉवर मेजचो.

$$\sqrt{0.1\times \frac{841}{40000}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

\frac{841}{400000} मेळोवंक 0.1 आनी \frac{841}{40000} गुणचें.

$$\sqrt{\frac{841}{400000}+0.3\left(-\frac{2.5}{100}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

10 न्युमरेटर आनी डिनोमिनेटर दोनूय गुणून \frac{2.5}{100} विस्तारीत करचो.

$$\sqrt{\frac{841}{400000}+0.3\left(-\frac{25}{1000}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

25 भायर काडून आनी रद्द करून एकदम उण्या संज्ञेत अपुर्णांक \frac{25}{1000} उणो करचो.

$$\sqrt{\frac{841}{400000}+0.3\left(-\frac{1}{40}\right)^{2}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

\frac{1}{1600} मेळोवंक 2 चो -\frac{1}{40} पॉवर मेजचो.

$$\sqrt{\frac{841}{400000}+0.3\times \frac{1}{1600}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

\frac{3}{16000} मेळोवंक 0.3 आनी \frac{1}{1600} गुणचें.

$$\sqrt{\frac{841}{400000}+\frac{3}{16000}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

\frac{229}{100000} मेळोवंक \frac{841}{400000} आनी \frac{3}{16000} ची बेरीज करची.

$$\sqrt{\frac{229}{100000}+0.4\times \left(\frac{2.5}{100}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

10 न्युमरेटर आनी डिनोमिनेटर दोनूय गुणून \frac{2.5}{100} विस्तारीत करचो.

$$\sqrt{\frac{229}{100000}+0.4\times \left(\frac{25}{1000}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

25 भायर काडून आनी रद्द करून एकदम उण्या संज्ञेत अपुर्णांक \frac{25}{1000} उणो करचो.

$$\sqrt{\frac{229}{100000}+0.4\times \left(\frac{1}{40}\right)^{2}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

\frac{1}{1600} मेळोवंक 2 चो \frac{1}{40} पॉवर मेजचो.

$$\sqrt{\frac{229}{100000}+0.4\times \frac{1}{1600}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

\frac{1}{4000} मेळोवंक 0.4 आनी \frac{1}{1600} गुणचें.

$$\sqrt{\frac{229}{100000}+\frac{1}{4000}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

\frac{127}{50000} मेळोवंक \frac{229}{100000} आनी \frac{1}{4000} ची बेरीज करची.

$$\sqrt{\frac{127}{50000}+0.2\times \left(\frac{5.5}{100}\right)^{2}}$$

10 न्युमरेटर आनी डिनोमिनेटर दोनूय गुणून \frac{5.5}{100} विस्तारीत करचो.

$$\sqrt{\frac{127}{50000}+0.2\times \left(\frac{55}{1000}\right)^{2}}$$

5 भायर काडून आनी रद्द करून एकदम उण्या संज्ञेत अपुर्णांक \frac{55}{1000} उणो करचो.

$$\sqrt{\frac{127}{50000}+0.2\times \left(\frac{11}{200}\right)^{2}}$$

\frac{121}{40000} मेळोवंक 2 चो \frac{11}{200} पॉवर मेजचो.

$$\sqrt{\frac{127}{50000}+0.2\times \frac{121}{40000}}$$

\frac{121}{200000} मेळोवंक 0.2 आनी \frac{121}{40000} गुणचें.

$$\sqrt{\frac{127}{50000}+\frac{121}{200000}}$$

\frac{629}{200000} मेळोवंक \frac{127}{50000} आनी \frac{121}{200000} ची बेरीज करची.

$$\sqrt{\frac{629}{200000}}$$

\frac{\sqrt{629}}{\sqrt{200000}} च्या वर्ग मूळाचो भागाकार म्हूण \sqrt{\frac{629}{200000}} च्या वर्गमूळाचो भागाकार परत बरोवचो.

$$\frac{\sqrt{629}}{\sqrt{200000}}$$

200000=200^{2}\times 5 गुणकपद काडचें. \sqrt{200^{2}}\sqrt{5} च्या वर्ग मूळाचो गुणाकार म्हूण \sqrt{200^{2}\times 5} च्या वर्गमूळाचो गुणाकार परत बरोवचो. 200^{2} चें वर्गमूळ घेवचें.

$$\frac{\sqrt{629}}{200\sqrt{5}}$$

न्युमरेटर आनी डिनोमिनेटर \sqrt{5} न गुणून \frac{\sqrt{629}}{200\sqrt{5}} चो डिनोमिनेटर रेशनलायझ तर्कसंगत करचो.

$$\frac{\sqrt{629}\sqrt{5}}{200\left(\sqrt{5}\right)^{2}}$$

\sqrt{5} चो वर्ग 5 आसा.

$$\frac{\sqrt{629}\sqrt{5}}{200\times 5}$$

\sqrt{629} आनी \sqrt{5} गुणूंक, वर्गमुळाच्या खाला संख्या गुणची.

$$\frac{\sqrt{3145}}{200\times 5}$$

1000 मेळोवंक 200 आनी 5 गुणचें.

$$\frac{\sqrt{3145}}{1000}$$